A hydraulic vehicle brake with an electrically actuable parking brake apparatus is known, for example, from the older international patent application of the applicant WO 2008/037738 A1, which is incorporated by reference. The special feature of the previously known vehicle brake consists in that the rolling bodies are arranged between two stops in the thread such that they can be moved to a limited extent, a spring element being arranged between the rolling bodies and one stop and making sliding of the rolling bodies possible during load-free actuation of the gear mechanism and making rolling of the rolling bodies possible during actuation of the gear mechanism under load. These features achieve a situation where the gear mechanism can be produced inexpensively. Here, the gear mechanism is configured as a two-stage step-down gear mechanism, one stage of the step-down gear mechanism having a self-locking action.